The treatment for the scattering by ionized impurities in a semiconductor using the partial wave technique is set up and applied using a square well for the attractive impurity and a square barrier to represent the repulsive impurity. For the case ka≪1 (where k is the wave number of the charge carriers and a is the range of the impurity potential), analytical solutions are obtained for the mobility, μ, and Hall coefficients applicable to nondegenerate semiconductors at low temperatures with high impurity content. The mean free time for scattering is a function of the parameters ka and (±2m*q2aℏ2D)12, where q is the charge of the carrier and D is the dielectric constant. The present treatment for reasonable choices of a yields limiting laws of μ∝T−12NI−13 for repulsive centers, while for attractive centers there are three possible limiting cases: μ1∝T−12NI−13, μ2∝T12NI−1 and μ3→∞. Case 2 refers to a form of resonance scattering and case 3 is the Ramsauer effect in semiconductors. These results are markedly different from previous formulas valid for ka≫1 which yield μ∝T32NI−1 for both attractive and repulsive centers.
Semiconductor Doping, Degenerate Doping & an Intoduction ...
Degenerate doping in semiconductors